Max-Margin

a linearly separable dataset admits infinitely many separating hyperplanes, and the perceptron will happily hand you whichever one it trips over first. 𐃏 the support vector machine asks a better question: of all the hyperplanes that separate the data, which one is farthest from everybody? the answer — the maximum-margin hyperplane — is determined by a handful of boundary points (the support vectors), drops out of a beautiful convex dual, and generalises via the kernel trick from lines to nearly anything.